In the field of image processing, it is often the case that an image must be resized for a desired application. For example, a particular printer may have a fixed resolution of 250 dpi (dots per inch). In order to print an image consisting of 500 by 750 pixels to a 4 by 6 inch print on such a printer, the image must be resized by a factor of 2. Likewise, many display devices have a fixed resolution in pixels per inch. In other words, the values of the image at locations between the original samples must be determined. This process of determining the value of an image signal at locations which are not coincident with the original samples of the image is called interpolation or resampling. The factor of interpolation, N, refers to the ratio of the sampling rate of the output image to the sampling rate of the input image. In the previous example, the interpolation factor N=2.
The process of interpolation produces an image of a desired number of rows and columns of pixels. However, the interpolation process involves “guessing” the signal value at many locations. As a result the interpolated image is generally not as high quality as an image originally captured at the desired resolution. For example, an image captured at 500×750 pixels and then interpolated to 1000×1500 pixels will generally appear softer and of lower quality than an image resulting from capturing that same scene at 1000×1500 pixels originally.
Because of the generally lower quality of interpolated images, it can be desirable to have knowledge of whether an image had been interpolated in order to better handle the image in later digital processing and other procedures. U.S. Pat. No. 6,904,180, to Gallagher, which is hereby incorporated herein by reference, discloses a method for determining whether a digital imaging channel is interpolated or non-interpolated using a signal related to values of neighboring pixels of an image. The method looks for peak in a Fourier Transform signal computed from an extracted signal having a periodicity indicative of interpolation. This method does not address the effects of past compression-decompression on an image.
With the advent of low-cost and high-resolution digital cameras and sophisticated editing software, digital images can be easily manipulated and altered. Digital forgeries, often have no visual clues of tampering and are indistinguishable from authentic photographs. As a result, photographs no longer hold the unique stature as a definitive recording of events. For example, in March of 2003 the Los Angeles Times published, on its front page, a dramatic photograph of a soldier directing an Iraqi citizen to take cover. The photograph, however, was a fake—it was digitally created by splicing together two photographs. This and similar incidents naturally lead one to wonder how many of the images seen every day have been digitally doctored. For more on digital forgeries.
While digital watermarking techniques have been proposed to authenticate images, the markings produced by these techniques have to be planted in the original images in advance. The markings are also susceptible to image processing operations, which may render the markings undetectable. There is therefore a need for a technique for detecting traces of digital tampering in the complete absence of any form of digital watermark or signature.
Although digital forgeries may leave no visual clues of having been tampered with, they may, nevertheless, alter the underlying statistics of an image. For example, consider the creation of a digital forgery that shows a pair of faces in the same image. Such an image could have been manufactured by compositing, such as, splicing a face from one original photograph and resampling it to match the composition of the destination image and inserting it. In order to create a convincing match, it is often necessary to resize, rotate, or stretch portions of the images. This process requires re-sampling or interpolating the original image onto a new sampling lattice. Although this resampling is often imperceptible, it modifies the statistical relationships of image pixel values, which when detected can be used as evidence of digital tampering. “Exposing digital forgeries by detecting traces of resampling”, A. C. Popescu and H. Farid, IEEE Transactions on Signal Processing, Vol. 53, No. 2, pages 758-767, 2005 is directed to detecting resampling due to forgeries.
Most digital images are either stored in compressed form or have gone through image compression at some point of its life. A number of block-based image compression techniques are known. The most common form of image compression is JPEG compression. Another block-based image compression is vector quantization (See R. M. Gray, “Vector Quantization,” IEEE ASSP Magazine, pages 4-29, (April 1984).) Block-based image compression produces artifacts that pose a challenge to the detection of digital watermarking and interpolation detection in images that have a history of having been compressed.
U.S. Pat. No. 6,643,410 to Yu et al., which is hereby incorporated herein by reference, discloses a method for detecting the extent of blocking artifacts in a digital image.
It would thus be desirable to provide methods and systems for detecting compositing, which can detect image interpolation even if an image was previously compressed.